Problem: Which of the following numbers is a factor of 146? ${2,5,12,13,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $146$ by each of our answer choices. $146 \div 2 = 73$ $146 \div 5 = 29\text{ R }1$ $146 \div 12 = 12\text{ R }2$ $146 \div 13 = 11\text{ R }3$ $146 \div 14 = 10\text{ R }6$ The only answer choice that divides into $146$ with no remainder is $2$ $ 73$ $2$ $146$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $146$ $146 = 2\times73 2 = 2$ Therefore the only factor of $146$ out of our choices is $2$. We can say that $146$ is divisible by $2$.